Nuprl Lemma : seteq_weakening
∀s1,s2:coSet{i:l}. ((s1 = s2 ∈ coSet{i:l}) ⇒ seteq(s1;s2))
Proof
Definitions occuring in Statement :
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
coSet_wf,
seteqweaken_wf
Rules used in proof :
hypothesis,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}s1,s2:coSet\{i:l\}. ((s1 = s2) {}\mRightarrow{} seteq(s1;s2))
Date html generated:
2018_07_29-AM-09_51_01
Last ObjectModification:
2018_07_20-PM-05_49_13
Theory : constructive!set!theory
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